We propose to use precise estimators of mutual information (MI) to find the least dependent components in a linearly mixed signal. On the one hand, this seems to lead to better blind source separation than with any other presently available algorithm. On the other hand, it has the advantage, compared to other implementations of "independent" component analysis (ICA), some of which are based on crude approximations for MI, that the numerical values of the MI can be used for (i) estimating residual dependencies between the output components; (ii) estimating the reliability of the output by comparing the pairwise MIs with those of remixed components; and (iii) clustering the output according to the residual interdependencies. For the MI estimator, we use a recently proposed k -nearest-neighbor-based algorithm. For time sequences, we combine this with delay embedding, in order to take into account nontrivial time correlations. After several tests with artificial data, we apply the resulting MILCA (mutual-information-based least dependent component analysis) algorithm to a real-world dataset, the ECG of a pregnant woman.

It has been thought that the capture of irregular moons--with non-circular orbits--by giant planets occurs by a process in which they are first temporarily trapped by gravity inside the planet's Hill sphere (the region where planetary gravity dominates over solar tides). The capture of the moons is then made permanent by dissipative energy loss (for example, gas drag) or planetary growth. But the observed distributions of orbital inclinations, which now include numerous newly discovered moons, cannot be explained using current models. Here we show that irregular satellites are captured in a thin spatial region where orbits are chaotic, and that the resulting orbit is either prograde or retrograde depending on the initial energy. Dissipation then switches these long-lived chaotic orbits into nearby regular (non-chaotic) zones from which escape is impossible. The chaotic layer therefore dictates the final inclinations of the captured moons. We confirm this with three-dimensional Monte Carlo simulations that include nebular drag, and find good agreement with the observed inclination distributions of irregular moons at Jupiter and Saturn. In particular, Saturn has more prograde irregular moons than Jupiter, which we can explain as a result of the chaotic prograde progenitors being more efficiently swept away from Jupiter by its galilean moons.

The discovery that many trans‐Neptunian objects exist in pairs, or binaries, is proving invaluable for shedding light on the formation, evolution and structure of the outer Solar system. Based on recent systematic searches it has been estimated that up to 10 per cent of Kuiper‐belt objects might be binaries. However, all examples discovered to date are unusual, as compared with near‐Earth and main‐belt asteroid binaries, for their mass ratios of the order of unity and their large, eccentric orbits. In this article we propose a common dynamical origin for these compositional and orbital properties based on four‐body simulations in the Hill approximation. Our calculations suggest that binaries are produced through the following chain of events. Initially, long‐lived quasi‐bound binaries form by two bodies getting entangled in thin layers of dynamical chaos produced by solar tides within the Hill sphere. Next, energy transfer through gravitational scattering with a low‐mass intruder nudges the binary into a nearby non‐chaotic, stable zone of phase space. Finally, the binary hardens (loses energy) through a series of relatively gentle gravitational scattering encounters with further intruders. This produces binary orbits that are well fitted by Kepler ellipses. Dynamically, the overall process is strongly favoured if the original quasi‐bound binary contains comparable masses. We propose a simplified model of chaotic scattering to explain these results. Our findings suggest that the observed preference for roughly equal‐mass ratio binaries is probably a real effect; that is, it is not primarily due to an observational bias for widely separated, comparably bright objects. Nevertheless, we predict that a sizeable population of very unequal‐mass Kuiper‐belt binaries is probably awaiting discovery.